Calculation of the glueball mass spectrum ofSU (2) andSU (3) non-abelian lattice gauge theories II:SU (3)

We calculate the glueball mass spectrum in theSU (3) lattice regularized gauge theory. We find fourlight glueballs: the 0⁺⁺, 2⁺⁺, 0^?+ and, most interestingly from the experimental point of view, the oddball 1^?+. We calculate the 0⁺⁺ and 2⁺⁺ masses over a range of β values and find thatboth states conform to continuum renormalization group behaviour to a very significant degree. The question of metastable states and temperature is addressed in detail. Finally we discuss and resolve contrary claims in the recent literature.     

Constructing local composite operators for glueball states from a confining Gribov propagator

The construction of BRST invariant local operators with the quantum numbers of the lightest glueball states, J ^PC=0⁺⁺,2⁺⁺,0^?+, is worked out by making use of an Euclidean confining renormalizable gauge theory. The correlation functions of these operators are evaluated by employing a confining gluon propagator of the Gribov type and shown to display a spectral representation with positive spectral densities. An attempt to provide a first qualitative analysis of the ratios of the masses of the lightest glueballs is also discussed.     

Variational computation of glueball masses in continuum QCD

We apply a field-theoretic Rayleigh-Ritz method to compute masses of the low-lying glueballs, with allowance for non-perturbative effects via condensate contributions to the gluon propagator. Since the gluon propagator is non-covariant, condensates of the form 〈TrAA〉 are allowed and must be introduced. Fitting the coupling constant and condensate parameter from the glueball candidates ι(1440) and θ(1690), we predict that mass (0⁺⁺) = 1320 ± 20 MeV, mass (2⁻⁺) = 1760 ± 40 MeV, at α_s = 0.46 ± 0.05 (with an error estimated by using a variety of trial wavepackets). Our result has the 0⁺⁺ glueball mass close to that of the isoscalar 0⁺⁺ states ε(1300) and g_s(1240), suggesting that at least one of these states (presumably he g_s(1240)) has a large-valence glue component.     

The experimental status of glueballs

Glueballs and other resonances with large gluonic components are predicted as bound states by Quantum Chromodynamics (QCD). The lightest (scalar) glueball is estimated to have a mass in the range from 1 to 2 GeV/c²; pseudoscalar and tensor glueballs are expected at higher masses. Many different experiments exploiting a large variety of production mechanisms have presented results in recent years on light mesons with J^PC=0⁺⁺, 0⁻⁺, and 2⁺⁺ quantum numbers. This review looks at the experimental status of glueballs. Good evidence exists for a scalar glueball which is mixed with nearby mesons, but a full understanding is still missing. Evidence for tensor and pseudoscalar glueballs are weak at best. Theoretical expectations of phenomenological models and QCD on the lattice are briefly discussed.     

Gluon jets from quarkonia

A detailed analysis is made within perturbative QCD of the decays into gluon jets of P-wave and S-wave quarkonia (J^PC = 0⁺⁺, 1⁺⁺, 2⁺⁺, 1^+? and 0^?+, 1^??). For all those states we compute to leading non-trivial order in α_s the conventional fraction f(?, δ) of the jet-like hadronic final states, characterized by the back-to-back cone of half angle δ, in which all but a small fraction ? of the total energy is emitted. To the same order we give also the average values of thrust momenta and spherocity distributions.     

Glueball masses and symmetry restoration inSU(3) lattice gauge theory: A high statistics Monte Carlo study

We calculate 0⁺⁺, 2⁺⁺ and 1^?+ correlation functions for a wide range of momenta in a high statisticsSU(3) study on an 8⁴ lattice: 28,000 sweeps at β=5.7 and 18,000 at β=5.9. We obtain an accurate confirmation of the restoration of the continuum relativistic dispersion relation,E ²=p ²+m ², and of rotational invariance. We obtain accurate 2⁺⁺ mass estimates up to two lattice spacings, and confirm consistency with asymptotic scaling. For the 1^?+ the results are much poorer and we can only present some very crude mass estimates. We compare our 0⁺⁺ data to our previous calculations with a source, and make some statements about the relative efficiencies of source and variational calculations in this range of couplings.     

A transverse gluonium potential model with Breit-fermi hyperfine effects

We introduce a potential model of bound transverse gluons with a fictitious constitutent mass. The gluonic Breit hamiltonian due to one gluon exchange is derived, and its effect on thegg spectrum is estimated; hyperfine corrections are large, but not nonperturbatively so. We find a degenerate (0⁺⁺, 0^?+) ground state and a first 2⁺⁺ excitation at ～1.2M ₀. Our list ofgg states disagrees with some sources, due to the absence of unphysical longitudinal degrees of freedom in the model.     

Sum rules for the decays of the c-even charmonium states

Sum rules for the decays of the C-even charmonium levels (¹S₀, ³P₀, ³P₂, ¹D₂) are derived. These rules are based on the asymptotic freedom of the quantum chromodynamics at small distances and on the analyticity. They refer to the various vacuum amplitudes involving products of charmed quark currents: electromagnetic current as well as currents with quantum numbers J^PC=0^?+,0⁺⁺,2⁺⁺,2^?+. The contribution of the continuum to some of the sum rules is small, and they are saturated by the contribution of the lowest charmonium levels. In this way we predict the widths of the two-photon decays of the charmonium states and estimate their total hadronic widths.     

The mass spectrum of 0−+, 0++, 1−-, 2++ mesons in the SU(4) and SU(8) scheme and prediction of new narrow resonances

A unified treatment of 0^?+, 0⁺⁺, 1^?-, 2⁺⁺ meson multiplets is provided, in the SU(4) and SU(8) scheme. The overall consistence is excellent and the existence of a new 1^?- resonance φ_c(2.835) is predicted.     

Spectral function sum rules for gluonic currents

We determine the masses and the decay amplitudes of the 2⁺⁺, 0^?+ and 0⁺⁺ gluonia in anSU(3) _c Yang-Mills theory. We estimate the so-called topological susceptibility of theU(1) sector. We discuss theSU(3) _F breaking effects to the η′(896) massrelation from current algebra and predict the η′ parameter values.     

Charmonium States in QCD-Inspired Quark Potential Model Using Gaussian Expansion Method

We investigate the mass spectrum and electromagnetic processes of charmonium system with the nonperturbative treatment for the spin-dependent potentials, comparing the pure scalar and scalar-vector mixing linear confining potentials. It is revealed that the scalar-vector mixing confinement would be important for reproducing the mass spectrum and decay widths, and therein the vector component is predicted to be around 22?%. With the state wave functions obtained via the full-potential Hamiltonian, the long-standing discrepancy in M1 radiative transitions of J/ψ and ψ′ are alleviated. This work also provides an inspection and suggestion for the possible cc? states among the copious higher charmonium-like states. Particularly, the newly observed X(4160) and X(4350) are found in the charmonium family mass spectrum as M(2¹ D ₂)?= 4164.9 MeV and M(3³ P ₂)?= 4352.4 MeV, which strongly favor the J ^PC ?=?2^?+, 2⁺⁺ assignments respectively. The corresponding radiative transitions, leptonic and two-photon decay widths have been also predicted theoretically for the further experimental search.     

Experimental constraints onJ PC=1−+,I=1, Hybrid mesons

Using data on coherent production of π⁺π⁺π^- systems in π⁺ collisions with nuclei we exclude the existence ofJ ^PC=1^?+,I=1, exotic hybrid mesons with masses below 1.5 GeV and widths greater than 20 MeV, provided that their primary coupling is to πρ systems. Hybrid states with just such properties have recently been predicted from arguments based on QCD sum rules. Our experimental limit is based on Primakoff production of these states, and on an argument using vector dominance to relate their radiative widths to πρ channels. There has been increasing interest of late in the existence of hybrid states, which, in the case of mesons, contain a valence gluon in addition to aq \(\bar q\) pair in a color-octet state [1–5]. The pursuit of spectroscopic gluon degrees of freedom has been strongly motivated by the general QCD picture of hadrons, as well as by many specific calculations based on QCD sum rules, lattice simulations, and more phenomenological approaches such as QCD-bag models. Although much effort, both thoretical and experimental, has been devoted to the spectroscopy of glueballs, for which several candidates exist [6], it has also been realized that hybrid states may be as amenable to discovery, and perhaps less ambiguous to interpretation.     

Evidence for two strangeonium resonances with JPC=1++ and 1+− in K−p interactions at 11 GeV/c

The results of a partial wave analysis of the low mass KK̄π system produced in the reactions K⁻p→K⁰_sK^±π^±Λ at 11 GeV/c using the LASS spectrometer are presented. Evidence is given for two ss̄ axial-vector meson states: one with quantum numbers J^PC = 1⁺⁺, mass ∼ 1530 MeV/c², and width ∼ 100 MeV/c², and the other with quantum numbers J^PC=1⁺⁻, mass ∼ 1380 MeV/c², and width ∼ 80 MeV/c². These states are good candidates to be the mostly strangeonium members of the ground state 1⁺⁺ and 1⁺⁻ nonets predicted by the quark model.     

Supersymmetric dual string theory: (III). Loops and renormalization

The mixing of 0^?+ glueballs (G) and ordinary ¯qq mesons is calculated in the MIT bag model. The result is that the η and η′ have probabilities 7% and 19%, respectively, of being pure glue-glue state. This has implications for the η-η′ mass difference, and allows a quantitative estimate of the widths for G(0^?+)→γγ and γp, which may help distinguish a glueball from ¯qq mesons.     

Increased statistics and observation of the gT,gT′, and gT′' 2++resonances in the Glueball enhanced channel π−p→φφn

In a new experiment we have obtained 3006 new events in the reaction π⁻p→φφn, approximately doubling the statistics which now total 6658. A refined partial wave analysis of the φφ system again reveals three resonances (g_T, g_T′, g_T′') with I^GJ^PC=0⁺2⁺⁺. The absence of the OZI suppression, and the observation of only three J^PC=2⁺⁺ states (g_T, g_T′, g_T′') which comprise virtually all the cross section are unusual characteristics of the data. The large φφn signal occurs over a mostly structureless and incoherent φK⁺K⁻n background. All these unusual characteristics are well explained if these states are produced by 1–3 glueballs (multigluon resonances).     

Low mass glueballs in the meson spectrum

The spectrum of bound states of gluons is discussed within the MIT bag model. We argue that (1) contrary to previous analysis there is no light exotic 1^?+ state in the two gluon sector, (2) experiments on the three gluon sector can clearly differentiate the bag model from other models, (3) the state seen in J/ψ radiative decays at 1.4 GeV is most likely a pseudoscalar glueball, and (4) there should be a second 2⁺⁺ state underneath the f(1270) resonance.     

SU(3) lattice Monte Carlo calculation of the glueball mass spectrum

We have calculated the glueball masses of various spins and parities in SU(3) gauge theory. Our first results give m_M(0⁺⁺)=(3.6±0.2)Λ_mom, m_E(0⁺⁺)=(4.3±0.3)Λ_mom, m(0^?+)=(7.2_?0.9^+1.6)Λ_mom, m_M(2⁺⁺)=(8.1±1.1)Λ_mom and m_E(2⁺⁺)=(8.3_?1.0^+1.6)Λ_mom as well as information on the glueball wave functions.     

Glueball spectroscopy from strong coupling expansions in hamiltonian lattice QCD

Masses of all the glueballs which are created by 6- or 7-link operators are calculated to order g^?8 in pure SU(3) hamiltonian lattice gauge theory. Several low-lying states are found with masses $\text{m(0}{}^{\mathrm{++1}}\text{)～ 1.4 m}{}_{\mathrm{<mtext>s</mtext>}}\text{, m(0}{}^{\mathrm{++7}}\text{) ～ 1.7 m}{}_{\mathrm{<mtext>s</mtext>}}$ (¹ and ⁷ stand for radial excitations and m_s is the mass of the lowest 0⁺⁺ state), . These values are obtained at the point g^?2 ? 0.8, which lies near the scaling region.     

3π resonances in 2− partial waves

The J^PC = 2^?+ partial wave intensities and their large phase changes prove the resonant nature of the A₃ meson (mass ≈ 1670 MeV, width ≈ 210 MeV). The decay modes are f⁰π, ?⁰π, and ?⁰π. Evidence is found for a further 2^? enhancement.     

New meson configuration in the bag model (I). First order energy spectrum of qqg states

Perturbative QCD in the bag is applied to unconventional configuration of quarks and gluons. The meson spectrum is computed to second order in the strong coupling. Exotic states with J^PC = 1^?+, 0^+?, 0^?? are found in the energy range 1.57 ? E ? 1.93 GeV.